HELMHOLTZ IN BERLIN 



has been thus shortly stated by Professor Riicker : l 

 ' From 1870 onwards, Helmholtz published an im- 

 portant series of papers on the theory of electro- 

 dynamics. His point of departure was the discussion 

 of the mutual action of two current elements. An 

 expression for the potential of two such elements had 

 been formulated by F. E. Neumann, which differed 

 from those deduced from the theories of W. \Veber 

 and Clerk Maxwell respectively. All three gave 

 identical results in the case of closed circuits. Tak- 

 ing the elder Neumann's formula as the groundwork 

 of his investigations, Helmholtz sought to find the 

 terms which must be added to it, so as to produce 

 the most general expression consistent with the 

 known behaviour of closed circuits. The result was 

 an expression consisting of the sum of two terms, 

 which were multiplied respectively by i + k and 

 i - ^, where k is an undetermined constant. The 

 expression is equivalent to that given by Weber 

 when k = - i, to that given by F. E. Neumann 

 when k = i, and is in accord with Maxwell's theory 

 when k = o. It was then proved that if k is 

 negative the equilibrium of electricity at best must 

 be unstable, so that motion, when once established, 

 would increase of its own accord, and lead to infinite 

 velocities and densities. The assumption was, in fact, 

 a violation of the law of the conservation of energy 



1 Riicker, Obituary Notice of Helmholtz, Proc. Roy. Sac., vol. lix., No. 

 355, P- 27- 



207 



